2013/11/29 by Nikolay Prodanov, Prodanov, Nikolay, Wolf B. Dapp +3 · 3 citations
Engineering · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Force Microscopy Techniques and Applications #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1311.7547
The description of elastic, nonadhesive contacts between solids with\nself-affine surface roughness seems to necessitate knowledge of a large number\nof parameters. However, few parameters suffice to determine many important\ninterfacial properties as we show by combining dimensional analysis with\nnumerical simulations. This insight is used to deduce the pressure dependence\nof the relative contact area and the mean interfacial separation \Δ\n\u and to present the results in a compact form. Given a proper unit\nchoice for pressure p, i.e., effective modulus E^* times the\nroot-mean-square gradient \g, the relative contact area mainly depends\non p but barely on the Hurst exponent H even at large p. When using the\nroot-mean-square height \h as unit of length, \Δ \u\nadditionally depends on the ratio of the height spectrum cutoffs at short and\nlong wavelengths. In the fractal limit, where that ratio is zero, solely the\nroughness at short wavelengths is relevant for \Δ \u. This limit,\nhowever, should not be relevant for practical applications. Our work contains a\nbrief summary of the employed numerical method Green's function molecular\ndynamics including an illustration of how to systematically overcome numerical\nshortcomings through appropriate finite-size, fractal, and discretization\ncorrections. Additionally, we outline the derivation of Persson theory in\ndimensionless units. Persson theory compares well to the numerical reference\ndata.\n